Investigating seepage in rough porous media fractures using fractional Brownian motion simulation

Authors

• LIU Weitao, College of Safety and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China;College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, ChinaFollow
• KONG Debin, College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, China;School of Resources and Safety Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaFollow
• MAO Qingfu, Wenshang Yiqiao Coal Mine Co., Ltd., Jining 272155, China
• ZHAO Jiyuan, College of Safety and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China
• GU Yulong, College of Safety and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China
• ZHANG Xiao, College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, China;Xinjiang Kalatongke Mining Co., Ltd., Altay Prefecture 836106, China

Abstract

Background Natural rock fractures are often partially filled with permeable materials such as silt and minerals under long-term geological and hydraulic actions, forming complex structures containing unfilled voids. The seepage characteristics of such fractures significantly influence petroleum extraction, mine water prevention, and the stability of underground engineering projects. Methods To reveal the underlying seepage mechanisms, this study generated rough profiles of unfilled voids with different fractal dimensions based on Fractional Brownian Motion. A theoretical expression for the overall permeability of partially filled fractures was derived, and a coupled free flow–porous medium flow numerical model was established. This framework was used to systematically investigate the effects of fracture pressure drop, residual aperture, and filling matrix permeability on the seepage behavior and overall permeability of partially filled fractures. Results and Conclusions The results indicate that: (1) The overall permeability of partially filled fractures remains stable under low pressure drops but decays under high pressure drops due to inertial effects; vortex induced by rough walls can reduce permeability by up to approximately 25.9%. (2) The residual aperture plays a dominant role in controlling fracture permeability and the effective hydraulic aperture, with its influence significantly stronger than that of the fractal dimension of roughness. As the residual aperture increases from 0.1 mm to 5 mm, the overall permeability exhibits nonlinear growth, spanning six orders of magnitude (from 10^–12 m² to 10^–6 m²). (3) The influence of filling matrix permeability can be divided into three stages: in the low-permeability stage (k<10^–10m²), flow is dominated by the unfilled void, and the overall permeability remains stable; in the intermediate stage (10^–10<k<10^–5m²), the overall permeability increases with matrix permeability, and the flow distribution approaches the geometric proportion; in the high-permeability stage (k>10^–5m²), the permeability growth slows and gradually stabilizes, with the influence of matrix permeability weakening as the residual aperture increases. (4) In the low filling matrix permeability stage (k<10^–10m²), the theoretical predictions of the overall permeability of partially filled fractures show good agreement with numerical simulations across varying fractal dimensions and residual apertures, demonstrating the model's effectiveness in representing the seepage behavior of such fractures.

Keywords

partially filled fracture, fractional Brownian motion, fractal dimension, permeability

DOI

10.12363/issn.1001-1986.26.01.0044

Recommended Citation

LIU Weitao, KONG Debin, MAO Qingfu, et al. (2026) "Investigating seepage in rough porous media fractures using fractional Brownian motion simulation," Coal Geology & Exploration: Vol. 54: Iss. 8, Article 13.
DOI: 10.12363/issn.1001-1986.26.01.0044
Available at: https://cge.researchcommons.org/journal/vol54/iss8/13

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